Finite Group Databasebeta

← #16787062

Subgroups — #16787062

Order 3328.

288 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 68 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13131205C212yesmaximal, complemented
2#13129784C212yesmaximal, complemented
3#13129770C212yesmaximal
4#13123480C211yesmaximal, characteristic
5C4×C13×#41C411yescharacteristic
6#11718895C411yescharacteristic
7#11718895C2211yescharacteristic
8#11718661—22no—
9#11718660C411yescharacteristic
10#11718660C2211yescharacteristic
11#11718586—22no—
12C4×#6099C2211yescharacteristic
13C2×C4×#1055C411yescharacteristic
14#11718284C2214yes—
15#11718233—22no—
16#11718232—22no—
17C2×C13×#41C2×C411yescharacteristic
18C4×Q8×C13—21no—
19C4×D4×C13—21no—
20C4×D4×C13—22no—
21C13×#117—21no—
22C13×#117C2×C411yescharacteristic
23C2×C42×C13—21no—
24C2×C42×C13C2×C411yescharacteristic
25C2×#6099C2×C411yescharacteristic
26C2×#6099C2311yescharacteristic
27C22×#1055C2×C411yescharacteristic
28C22×#1055C2×C411yescharacteristic
29#88106—24no—
30C22⋊#1055—22no—
31C22⋊#1055—22no—
32C4⋊#1055—22no—
33C4⋊#1055—22no—
34#88043D412yes—
35C4×#1055—21no—
36C4×#1055—21no—
37C4×#1055D412yes—
38#11524—131nomaximal, Sylow
39C13×#41—41no—
40C13×#41—41no—
41C2×Q8×C13M1611yescharacteristic
42C2×D4×C13—21no—
43C2×D4×C13M1611yescharacteristic
44C22×C4×C13—22no—
45C22×C4×C13—21no—
46C22×C4×C13—21no—
47C22×C4×C13C22×C411yescharacteristic
48C13×C4⋊C4—22no—
49C13×C4⋊C4—21no—
50C13×C22⋊C4—22no—
51C13×C22⋊C4M1612yes—
52C42×C13—22no—
53C42×C13—21no—
54C42×C13—21no—
55C42×C13C22⋊C411yescharacteristic
56C42×C13C22⋊C411yescharacteristic
57#6099—41no—
58#6099—41no—
59C2×#1055—21no—
60C2×#1055—21no—
61C2×#1055—41no—
62C2×#1055—41no—
63C2×#1055C22⋊C412yes—
64C2×#1055C2×D412yes—
65#6092—44no—
66#2922—131no—
67#2165—132no—
68#1328—132no—
69#1321—132no—
70C23×C13—21no—
71C23×C13C2×M1611yescharacteristic
72Q8×C13—41no—
73D4×C13—41no—
74D4×C13—42no—
75C2×C4×C13—21no—
76C2×C4×C13—21no—
77C2×C4×C13—21no—
78C2×C4×C13—22no—
79C2×C4×C13—21no—
80C2×C4×C13—21no—
81C2×C4×C13—42no—
82C2×C4×C13—44no—
83C2×C4×C13—41no—
84C2×C4×C13—41no—
85C2×C4×C13C2×C22⋊C411yescharacteristic
86C2×C4×C13C2×M1611yescharacteristic
87#1055—22no—
88#1055—22no—
89#1055—41no—
90#1055—41no—
91C4×#41#26111yescharacteristic
92#433—262no—
93#431—262no—
94#424—131no—
95#424—131no—
96#408—131no—
97#408—131no—
98C4×M16—131no—
99C2×C4×C8—131no—
100#364—262no—
101#349—134no—
102#347—262no—
103C22×C13—21no—
104C22×C13—41no—
105C22×C13—42no—
106C22×C13—41no—
107C22×C13#40711yescharacteristic
108C4×C13—22no—
109C4×C13—21no—
110C4×C13—42no—
111C4×C13—41no—
112C4×C13—41no—
113C4×C13#41011yescharacteristic
114C4×C13#41311yescharacteristic
115C2×#41C2×#26111yescharacteristic
116C2×M16—131no—
117C2×M16—131no—
118C22×C8—131no—
119C22×C8—131no—
120C4×Q8—21no—
121C4×D4—21no—
122C4×D4—22no—
123#117—21no—
124#117C2×#26111yescharacteristic
125C2×C42—21no—
126C2×C42C2×#26111yescharacteristic
127M32—264no—
128C4⋊C8—262no—
129C4⋊C8—262no—
130C22⋊C8—262no—
131C22⋊C8—262no—
132#97—132no—
133C4×C8—132no—
134C4×C8—261no—
135C4×C8—261no—
136C2×C13—21no—
137C2×C13—41no—
138C2×C13—81no—
139C2×C13#146411yescharacteristic
140#41—41no—
141#41—41no—
142C2×Q8#612211yescharacteristic
143C2×D4—21no—
144C2×D4#612211yescharacteristic
145C22×C4—22no—
146C22×C4—21no—
147C22×C4—21no—
148C22×C4C22×#26111yescharacteristic
149M16—521no—
150M16—521no—
151C2×C8—132no—
152C2×C8—132no—
153C2×C8—261no—
154C2×C8—261no—
155C2×C8—521no—
156C2×C8—521no—
157C4⋊C4—22no—
158C4⋊C4—21no—
159C22⋊C4—22no—
160C22⋊C4#612212yes—
161C42—22no—
162C42—21no—
163C42—21no—
164C42C22⋊#26111yescharacteristic
165C42C22⋊#26111yescharacteristic
166C16—524no—
167C13#1152411yescharacteristic, complemented, Sylow
168C23—21no—
169C23C2×#612211yescharacteristic
170Q8—41no—
171D4—41no—
172D4—42no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—22no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—42no—
180C2×C4—44no—
181C2×C4—41no—
182C2×C4—41no—
183C2×C4C2×#612211yescharacteristic
184C2×C4C2×C22⋊#26111yescharacteristic
185C8—262no—
186C8—262no—
187C8—521no—
188C8—521no—
189C22—21no—
190C22—41no—
191C22—42no—
192C22—41no—
193C22#1171916911yescharacteristic
194C4—22no—
195C4—21no—
196C4—42no—
197C4—41no—
198C4—41no—
199C4#1171911611yescharacteristic
200C4#1171913211yescharacteristic
201C2—21no—
202C2—41no—
203C2—81no—
204C2#1313008711yescharacteristic
subgroupG/H
centerC4#11719116
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC4×C13×#41C4
socleC2×C13#1464
prime radicalC2×C13×#41C2×C4
cosocleC2×#6099C23
hypercenterC4×#41#261
hypocenterC13#11524
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C42 ◁ C2×C42 ◁ C4×#41

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #13131205C2semidirect
2. #13129784C2semidirect
167. C13#11524semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#131312052
#131297842
#131297702
#131234802
#1152413